$A$ $100 \; W$ sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is $589 \; nm$.
$(a)$ What is the energy per photon associated with the sodium light?
$(b)$ At what rate are the photons delivered to the sphere?

(N/A) Given: Power $P = 100 \; W$, Wavelength $\lambda = 589 \; nm = 589 \times 10^{-9} \; m$, Planck's constant $h = 6.63 \times 10^{-34} \; J \cdot s$, Speed of light $c = 3 \times 10^8 \; m/s$.
$(a)$ The energy per photon $E$ is given by the formula $E = \frac{hc}{\lambda}$.
Substituting the values: $E = \frac{(6.63 \times 10^{-34} \; J \cdot s) \times (3 \times 10^8 \; m/s)}{589 \times 10^{-9} \; m} \approx 3.376 \times 10^{-19} \; J$.
$(b)$ The rate of delivery of photons $n$ is given by $n = \frac{P}{E}$.
Substituting the values: $n = \frac{100 \; W}{3.376 \times 10^{-19} \; J} \approx 2.96 \times 10^{20} \; \text{photons/second}$.